Quick answer: The unofficial totk-pc-recomp project now has a native Linux build. Steam Deck HQ tested it on a Steam Deck and got 60 FPS in early areas but 30 to 40 FPS in the open world. It needs your own legally dumped copy of the game.
The unofficial Tears of the Kingdom recompilation can now run natively on the Steam Deck. The project is called totk-pc-recomp, made by valentderah, and it turns the Switch game into a native x86-64 program for Windows and Linux instead of running it through an emulator. Steam Deck HQ has now tested the new Linux version on a Deck.
Linux support arrived in version 0.2.1 on October 31. The setup comes as an AppImage that builds the game from your own files into a folder you choose, and on a Steam Deck you run it in Desktop Mode. The project lists Linux 6.7 or later and SteamOS 3 among its requirements. Steam Deck HQ says the result is a Linux executable you can add to Steam.
Performance is a mixed bag so far. At the default settings, 1280x800 with an 83% render scale, Steam Deck HQ saw 60 FPS in the early, contained areas. In the open world it sat around 30 to 40 FPS, with drops under 30 while falling through the sky even at a 60% render scale. Shadows on the ground also flickered. Steam Deck HQ says it wouldn't call it playable or recommended on the Deck yet, but it already runs significantly better than emulation.
The project itself says it's in early development, with visual bugs and crashes still expected. Its notes also say most of the code is written by AI coding agents under the maintainer's direction.
No game files are included. You need your own legally obtained copy of Tears of the Kingdom, dumped from your own console, with the 1.1.0, 1.2.1 or 1.4.3 update, and the project doesn't explain how to get those files. It's the same approach as the unofficial Metroid Dread recomp I covered in October.